Example 14 
It turns out that the two formulations of CWA shown in
Example REF  are in fact both uniformly CWV-equivalent and
uniformly WV-equivalent ELPs. This can be verified by constructing the
relevant UE-functions. Let \(\Pi _{\text{Gelfond}} = (\mathcal {A}, \mathcal {E},\mathcal {R}_{\text{Gelfond}})\)  be the formulation of the CWA from
[1]}, and \(\Pi _{\text{ShenEiter}} = (\mathcal {A}, \mathcal {E},\mathcal {R}_{\text{ShenEiter}})\)  be the formulation from [2]}, where
\(\mathcal {A}= \lbrace  p^{\prime }, p \rbrace \)  and \(\mathcal {E}= \lbrace  \mathbf {not}\,p, \mathbf {not}\,\lnot p \rbrace \) . Omitting all
combinations of epistemic guesses and sets of facts where the UE-functions
return \(\emptyset \) , the UE-functions, for both \(W \in \lbrace  \text{WV}, \text{CWV}\rbrace \) , look as follows:
\(\mathcal {U}\mathcal {E}^W_{\Pi _{\text{Gelfond}}} & =\mathcal {U}\mathcal {E}^W_{\Pi _{\text{ShenEiter}}} = \lbrace \\& ( \lbrace  \mathbf {not}\,p \rbrace , \emptyset , \lbrace  \lbrace  p^{\prime } \rbrace  \rbrace  ),\\& ( \lbrace  \mathbf {not}\,p \rbrace , \lbrace  p^{\prime } \rbrace , \lbrace  \lbrace  p^{\prime } \rbrace  \rbrace  ),\\& ( \lbrace  \mathbf {not}\,\lnot p \rbrace , \lbrace  p \rbrace , \lbrace  \lbrace  p^{\prime }, p \rbrace  \rbrace  ),\\& ( \lbrace  \mathbf {not}\,\lnot p \rbrace , \lbrace  p^{\prime }, p \rbrace , \lbrace  \lbrace  p^{\prime }, p \rbrace  \rbrace  )\\\rbrace \) 
